Details
Original language | English |
---|---|
Pages (from-to) | 1419-1433 |
Number of pages | 15 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 29 |
Issue number | 6 |
Publication status | Published - Nov 1998 |
Externally published | Yes |
Abstract
We show existence and uniqueness of classical solutions for the motion of immersed hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a sphere, we prove that the solution exists globally and converges exponentially fast to a sphere. Furthermore, we provide numerical simulations showing the creation of singularities for immersed curves.
Keywords
- Center manifolds, Free boundary problem, Immersed hypersurfaces, Maximal regularity, Mean curvature, Numerical simulations, Surface diffusion
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Mathematical Analysis, Vol. 29, No. 6, 11.1998, p. 1419-1433.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The surface diffusion flow for immersed hypersurfaces
AU - Escher, Joachim
AU - Mayer, Uwe F.
AU - Simonett, Gieri
PY - 1998/11
Y1 - 1998/11
N2 - We show existence and uniqueness of classical solutions for the motion of immersed hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a sphere, we prove that the solution exists globally and converges exponentially fast to a sphere. Furthermore, we provide numerical simulations showing the creation of singularities for immersed curves.
AB - We show existence and uniqueness of classical solutions for the motion of immersed hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a sphere, we prove that the solution exists globally and converges exponentially fast to a sphere. Furthermore, we provide numerical simulations showing the creation of singularities for immersed curves.
KW - Center manifolds
KW - Free boundary problem
KW - Immersed hypersurfaces
KW - Maximal regularity
KW - Mean curvature
KW - Numerical simulations
KW - Surface diffusion
UR - http://www.scopus.com/inward/record.url?scp=0032379074&partnerID=8YFLogxK
U2 - 10.1137/S0036141097320675
DO - 10.1137/S0036141097320675
M3 - Article
AN - SCOPUS:0032379074
VL - 29
SP - 1419
EP - 1433
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 6
ER -